Examples of a combination known in the art of catalyst components for a highly stereoregular polymerization of an α-olefin are as follows:                (1) a combination of (i) a catalyst component produced by supporting a tetravalent titanium halide on a magnesium halide, (ii) an organoaluminum compound (promoter), and (iii) an organosilicon compound (third component) (JP 57-63310A, JP 58-83006A and JP 61-78803A);        (2) a combination of (i) a trivalent titanium compound-containing solid catalyst component produced by a process comprising the steps of (i-1) reducing a titanium compound with an organomagnesium compound in the presence of an organosilicon compound and an ester compound to produce a first solid product, (i-2) contacting the first solid product with an ester compound to produce a second solid produce, and (i-3) contacting the second solid product with a halogenation compound (for example, titanium tetrachloride) and an internal electron donor (for example, an ether compound, and a mixture thereof with an ester compound), (ii) an organoaluminum compound (promoter), and (iii) an external electron donor (third component) (JP 7-216017A); and        (3) a combination of (i) a trivalent titanium compound-containing solid catalyst component produced by a process comprising the steps of (i-1) reducing a titanium compound with an organomagnesium compound in the presence of an organosilicon compound and an ester compound to produce a first solid product, and (i-2) contacting the first solid product with a halogenation compound (for example, titanium tetrachloride), an internal electron donor (for example, an ether compound, and a mixture thereof with an ester compound), and an organic acid halide compound, (ii) an organoaluminum compound (promoter), and (iii) an external electron donor (third component) (JP 10-212319A).        